(1+iV3)"+(1-i/3)" %3D 2n+1 Sin(- 3 2" Cos( ) 3. 2n+ Cos( 3. 2" Sin 3. (1-V3

Q: x=-2+4 cos 0 and y=1+5 sin 0

A:

Q: 8. (a) 2e' (cos 3t – 3 sin 3t) (b) 3e-2 (sinh 2t – 2 cosh 2t)

A: Given functions: (a) 2etcos3t-3sin3t (b) 3e-2tsinh2t-2cosh2t   We know that,…

Q: 2 cos @ dӨ . 1- sin 0

A:

Q: 4. Find the general solution of the equation: cosr– sin 2x =0

A: Use general solution

Q: cos(2α) = − sin α with 0 ≤ α < 2π.

A:

Q: Find the solution of sin² (x) – 4sin (x) – 1 = 0 for all angles between 0 and 2n.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: (4) = - V2 -1 cos 4

A: Given,            cos-122=-π4

Q: Find the solution set of sin (2r) – cos² x = 0 on the interval [0, 27).

A:

Q: 7. Solve the equation over the interval [0,2n) cos? 0 – sin? 0 = 1- sin 0

A: Given query is to solve the equation and find the value of theta.

Q: 2 | [ cos ti- sin 7t j+sin 6t k]

A: Given :

Q: Find all solutions of the equation 2 cos x – V3 = 0. on interval [0, 27) x =

A:

Q: 4 cos 2x + 10 sin x – 7 = 0?

A:

Q: 2 - ƒ (t) = sin 0.5t + ²⁄t – 3 8 cos 32t

A:

Q: Show work.

A:

Q: 4. sin (5x + 22) = cos (4x + 14). Find x.

A: Equation is given by                sin(5x+22)= cos(4x+14)   ---(1)       formula which is to be…

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

A:

Q: 3nt 3nt s = sin 2 + cos 2 %3D

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: 3 Find sin 2x, cos 2x, and tan 2.x if cos.x = and x terminates in quadrant II. V10 sin 2x %3D

A: given

Q: COS x (5) dx (1+ sin x)5

A: ∫cosx(1+sinx)5dx

Q: 2. Solve for x the equation sin1 3x - cos1 2x = 6

A:

Q: the sum of sin h 2x and cos h 2x

A:

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

A:

Q: 2 + 3 sin 2x The value of 3x dx equals 1+ cos 2x

A:

Q: Im cos 2x + sin 2x} %3D Cos 4i - 4

A: To find: The imaginary part of -x4icos 2x+x4sin 2x. Concept used: If the complex number is written…

Q: 3. у"-2у'— sin 4x 1 cos 4x 40 1 sin 4x 20 Ans. y= c, + c,e²* + -

A: To find: The general solution of differential equation. Given: The differential equation is…

Q: 15 Find sin 2x, cos 2x, and tan 2x if cosx=- and x terminates in quadrant II. 17 sin 2x cos 2x %3D…

A:

Q: 4. (cos? 6x + sin 6x – sin³ 6x)Zdx (Hint:factor out sin 6x first) 3 -

A: We need to evaluate ∫cos26x+sin6x-sin36x12dx Using the identity  cos2y+sin2y=1⇒cos2y=1-sin2y…

Q: 2ä + 2i + x =1 with x(0) = 0 and ¿(0) = 2 Answer: x(t) = 1+ 3e-0.5t sin 0.5t – e-0.5t cos 0.5t

A:

Q: ( 4x³- 6x +5 2+3 cos x dx. 9. Find sin?

A:

Q: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

A:

Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: 15 Find sin 2x, cos 2x, and tan 2x if cos.xr= and x terminates in quadrant IV. 17 sin 2x cos 2x !!…

A:

Q: 3 1. cos x - 5 dx -3

A: The given integral is ∫-34 cosx-3x5dx. Evaluate as follows.

Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: Solve 1 – sin (A)+1= 2 cos(A) over 0, 27) -

A:

Q: у%3D sin(4x — 2) cos (4x + 2) || -

A: topic - derivative

Q: Solve the equation on the interval 0se<2x. sin 0= 6( cos (-e)-1) %3D

A: The solution is given below

Q: 3. sin(2x - 6) = cos(4x + 18) %3D

A:

Q: Solve the equation for 0 <0 < 2 . cos 0 – v2 cos 0 = 2 cos 0 sin 0 + cos 0

A: Do not cancell the common terms on both sides.

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: 5. Find all solutions of the equation 2 cos2 x - sin x = 1

A: Solution -    Given equation -  2cos2x-sinx=1                        ........................(1) We…

Q: Solve this equation for exact solutions over the interval [ 0, 2n ) : 2 cos 0 sin 0 = 0

A:

Q: 2. cos(4x) = 1 – 8(sin(x))²(cos(x))²

A:

Q: 1 In 3n 1 sin (3x) [cos"-1 (3r) sin (3r) + 3(n – 1)In-2] %3D I1 = %3D - 3 What is I, ?

A: Given : In = (1/3n)  [cosn-1 (3x) sin (3x) + 3(n − 1)In-2 ]  I₁ =  (1/3n)sin (3x)

Q: Find all solutions of the equation cos 2x + cos x in the interval [0,2x).

A:

Q: How would you evaluate∫cos2 x sin3 x dx?

A: Given: ∫cos2xsin3xdx

Q: Solve for 0 with 0 E [0, 27) 2 cos? 0-5 sin 0-4 0

A:

Q: Solve the equation on the interval [0,2π). Cos x- 2cos x sin x=0

A:

Q: .2 sin x- cos cos x = 0 %3D

A: Explanation of the answer is as follows

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.